Optimizing place-and-routing using a random normalized polish expression

ABSTRACT

Simultaneous automatic placement and routing speeds up implementation an integrated circuit layout and improves the resulting layout such that the layout is more compact, has reduced parasitics, and has improved circuit performance characteristics (e.g., power, frequency, propagation delay, gain, and stability). A technique generates solutions based on random normalized polish expression, and includes cost considerations based on routing of interconnect.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 15/950,112, filed Apr. 10, 2018, issued as U.S. Pat. No.10,726,184 on Jul. 28, 2020, which is a continuation of U.S. patentapplication Ser. No. 13/270,085, filed Oct. 10, 2011, issued as U.S.Pat. No. 9,940,421 on Apr. 10, 2018, which claims priority to U.S.patent application 61/392,021, filed Oct. 11, 2010. These applicationsare incorporated by reference along with all other references cited inthis application.

BACKGROUND OF THE INVENTION

The present invention relates to the field of electronic designautomation for integrated circuits, and in particular, to simultaneousplace and route for analog design.

Integrated circuits are important building blocks of the information ageand are critical to the information age, affecting every industryincluding financial, banking, legal, military, high technology,transportation, telephony, oil, medical, drug, food, agriculture,education, and many others. Integrated circuits such as DSPs,amplifiers, voltage converters, DRAMs, SRAMs, EPROMs, EEPROMs, Flashmemories, microprocessors, ASICs, and programmable logic are used inmany applications such as computers, networking, telecommunications, andconsumer electronics.

Consumers continue to demand greater performance in their electronicproducts. For example, higher speed computers will provide higher speedgraphics for multimedia applications or development. Higher speedinternet web servers will lead to greater on-line commerce includingon-line stock trading, book sales, auctions, and grocery shopping, justto name a few examples. Higher performance integrated circuits willimprove the performance of the products in which they are incorporated.

Large modern day integrated circuits have millions of devices includinggates and transistors and are very complex. As process technologyimproves, more and more devices may be fabricated on a single integratedcircuit, so integrated circuits will continue to become even morecomplex with time. To meet the challenges of building more complex andhigher performance integrated circuits, software tools are used. Thesetools are in an area commonly referred to as computer aided design(CAD), computer aided engineering (CAE), or electronic design automation(EDA). There is a constant need to improve these electronic automatictools in order to address the desire to for higher integration andbetter performance in integrated circuits.

An integrated circuit may be specified using a netlist and a layout. Thenetlist provides information about devices or components of theintegrated circuit and their connectivity. The integrated circuit layoutor integrated circuit mask layout is the representation of an integratedcircuit in terms of planar geometric shapes, patterns, and features thatcorrespond to shapes used in a mask to fabricate the circuit. A designengineer or mask designer may create the layout the integrated circuit.Some features in the layout or certain masks may be automaticallygenerated, such as automatic placement of elements and automatic routingof these elements.

Therefore, there is a need for improved placing and routing circuitry,especially for analog circuits.

BRIEF SUMMARY OF THE INVENTION

Simultaneous automatic placement and routing speeds up implementation anintegrated circuit layout and improves the resulting layout such thatthe layout is more compact, reduced parasitics, and improved circuitperformance characteristics (e.g., power, frequency, propagation delay,gain, and stability).

Other objects, features, and advantages of the present invention willbecome apparent upon consideration of the following detailed descriptionand the accompanying drawings, in which like reference designationsrepresent like features throughout the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a system of the present invention for performing electroniccircuit design, including automatic simultaneous placement and routing.

FIG. 2 shows a simplified system block diagram of computer system usedin implementation of the present invention.

FIG. 3 shows a simplified functional block diagram of an exemplary EDAsystem incorporating aspects of the present invention.

FIGS. 4A-4B show an example of a simultaneous place and route.

FIGS. 5A-5B show an example of a simultaneous place and route.

FIGS. 6A-6B show an example of a simultaneous place and route.

FIGS. 7A-7C show an example of a simultaneous place and route.

FIGS. 8A-8B show an example of a simultaneous place and route.

FIGS. 9A-9D show an example of a simultaneous place and route.

FIG. 10 shows an integrated circuit design flow.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows an electronic design automation (EDA) system of the presentinvention for designing an electronic circuit or integrated circuit,including automatic simultaneous placement and routing. In anembodiment, the invention is software that executes on a computerworkstation system, such as shown in FIG. 1. FIG. 1 shows a computersystem 101 that includes a monitor 103, screen 105, enclosure 107,keyboard 109, and mouse 111. Mouse 111 may have one or more buttons suchas mouse buttons 113. Enclosure 107 (may also be referred to as a systemunit, cabinet, or case) houses familiar computer components, some ofwhich are not shown, such as a processor, memory, mass storage devices117, and the like.

Mass storage devices 117 may include mass disk drives, floppy disks,magnetic disks, optical disks, magneto-optical disks, fixed disks, harddisks, CD-ROMs, recordable CDs, DVDs, recordable DVDs (e.g., DVD-R,DVD+R, DVD-RW, DVD+RW, HD-DVD, or Blu-ray Disc), flash and othernonvolatile solid-state storage (e.g., USB flash drive),battery-backed-up volatile memory, tape storage, reader, and othersimilar media, and combinations of these.

A computer-implemented or computer-executable version or computerprogram product of the invention may be embodied using, stored on, orassociated with computer-readable medium. A computer-readable medium mayinclude any medium that participates in providing instructions to one ormore processors for execution. Such a medium may take many formsincluding, but not limited to, nonvolatile, volatile, and transmissionmedia. Nonvolatile media includes, for example, flash memory, or opticalor magnetic disks. Volatile media includes static or dynamic memory,such as cache memory or RAM. Transmission media includes coaxial cables,copper wire, fiber optic lines, and wires arranged in a bus.Transmission media can also take the form of electromagnetic, radiofrequency, acoustic, or light waves, such as those generated duringradio wave and infrared data communications.

For example, a binary, machine-executable version, of the software ofthe present invention may be stored or reside in RAM or cache memory, oron mass storage device 117. The source code of the software of thepresent invention may also be stored or reside on mass storage device117 (e.g., hard disk, magnetic disk, tape, or CD-ROM). As a furtherexample, code of the invention may be transmitted via wires, radiowaves, or through a network such as the Internet.

FIG. 2 shows a system block diagram of computer system 101 used toexecute software of the present invention. As in FIG. 1, computer system101 includes monitor 103, keyboard 109, and mass storage devices 117.Computer system 101 further includes subsystems such as centralprocessor 202, system memory 204, input/output (I/O) controller 206,display adapter 208, serial or universal serial bus (USB) port 212,network interface 218, and speaker 220. The invention may also be usedwith computer systems with additional or fewer subsystems. For example,a computer system could include more than one processor 202 (i.e., amultiprocessor system) or the system may include a cache memory.

The processor may be a dual core or multicore processor, where there aremultiple processor cores on a single integrated circuit. The system mayalso be part of a distributed computing environment. In a distributedcomputing environment, individual computing systems are connected to anetwork and are available to lend computing resources to another systemin the network as needed. The network may be an internal Ethernetnetwork, Internet, or other network.

Arrows such as 222 represent the system bus architecture of computersystem 101. However, these arrows are illustrative of anyinterconnection scheme serving to link the subsystems. For example,speaker 220 could be connected to the other subsystems through a port orhave an internal connection to central processor 202. Computer system101 shown in FIG. 1 is but an example of a computer system suitable foruse with the present invention. Other configurations of subsystemssuitable for use with the present invention will be readily apparent toone of ordinary skill in the art.

Computer software products may be written in any of various suitableprogramming languages, such as C, C++, C#, Pascal, Fortran, Perl, Matlab(from MathWorks, Inc.), SAS, SPSS, Java, JavaScript, and AJAX. Thecomputer software product may be an independent application with datainput and data display modules. Alternatively, the computer softwareproducts may be classes that may be instantiated as distributed objects.The computer software products may also be component software such asJava Beans (from Oracle) or Enterprise Java Beans (EJB from Oracle).

An operating system for the system may be one of the Microsoft Windows®family of operating systems (e.g., Windows 95, 98, Me, Windows NT,Windows 2000, Windows XP, Windows XP x64 Edition, Windows Vista, Windows7, Windows CE, Windows Mobile), Linux, HP-UX, UNIX, Sun OS, Solaris, MacOS X, Alpha OS, AIX, IRIX32, or IRIX64, or combinations of these.Microsoft Windows is a trademark of Microsoft Corporation. Otheroperating systems may be used. A computer in a distributed computingenvironment may use a different operating system from other computers.

Furthermore, the computer may be connected to a network and mayinterface to other computers using this network. For example, eachcomputer in the network may perform part of the task of the many seriesof steps of the invention in parallel. Furthermore, the network may bean intranet, internet, or the Internet, among others. The network may bea wired network (e.g., using copper), telephone network, packet network,an optical network (e.g., using optical fiber), or a wireless network,or any combination of these. For example, data and other information maybe passed between the computer and components (or steps) of a system ofthe invention using a wireless network using a protocol such as Wi-Fi(IEEE standards 802.11, 802.11a, 802.11b, 802.11e, 802.11g, 802.11i, and802.11n, just to name a few examples). For example, signals from acomputer may be transferred, at least in part, wirelessly to componentsor other computers.

FIG. 3 shows a simplified functional block diagram of an exemplary EDAsystem 300 incorporating aspects of the present invention. The EDAsystem includes a number of software tools, any of which may access ashaped-based database model 301 containing an integrated circuit design,or one or more portions of an integrated circuit design. The EDA systemprovides such tools as a graphical user interface 302, global router304, manual editor 306, detail router 308, engineering change option(ECO) engine 310, timing-driven routing engine 312, extraction engine314, data export interface 318, and DSM process engine 320. An EDAsystem may include any number of the system tools shown in FIG. 3, andin any combination. Further, the EDA system may include additional toolsnot shown in FIG. 3.

An EDA system may be a grid-based system or shape-based system. Agrid-based system relies heavily on the concept of a grid and routinggrids. Gridded modeling, however, becomes difficult to implementsuccessfully as the routing and feature sizes become smaller. The amountof data increases according to a square law, which means that tasksbecome increasingly more computationally complex and time-consuming asthe amount of data increase. As feature sizes in integrated circuitscontinue to shrink, more features or geometries may be fitted into thesame unit area of an integrated circuit. Therefore, it is important foran EDA system to handle increasingly complex integrated circuits andprovide output or results quickly.

The techniques of the invention are especially suited for a shaped-basedsystem, which may also be referred to as a gridless system. Ashape-based system has no defined cell size. Each cell, or expansionarea, is as large as possible. In brief, a shape-based system can expandedges, which means that an edge of an enclosing rectangle (or otherpolygon) may be expanded in the direction of the edge as far as desireduntil the edge finds an obstacle. This may be referred to as a “flood”operation.

The shape may be representative of any polygon. For example, the shapemay be a rectangle. The shape may be representative of any polygon ofthe integrated circuit, such as a net, contact, via, transistor gate, ortransistor active area. Blocked edges are edges that cannot be extendedbecause they are blocked by a perimeter of another rectangle, such asanother segment, net, or obstacle. Once an obstacle is encountered, thena shape-based approach floods around the obstacle—making a ninety degreeor other angle (any angle may be used such as 30 degrees, 35 degrees, 36degrees, 42 degrees, 45 degrees, or 60 degrees) turns as needed to routearound the obstacle.

Chip design, be it analog, custom or digital, will increasingly sufferfrom timing and signal integrity issues, and in particular crosstalk, asgeometries continue to decrease and ever more fine wires are introduced.Gridded solutions are not flexible enough to resolve these issues, letalone achieve a high rate of routing completion. A high performancetiming and crosstalk-driven routing solution will become a mandatoryrequirement in physical design.

The grid-based approach offers fast routing but requires customizationto handle off-grid connections and is inefficient for post-route timingand signal integrity optimizations. When net widths and spacings must bechanged to reduce resistance or cross-talk, grid-based approaches wastespace by moving nets to the next available grid and waste time byresorting to rip-up and re-route techniques. Gridded systems are notgood at irregular intervals, irregular spacings, or routing things thatdo not fit onto a regular grid.

The gridless approach easily handles off-grid connections and isefficient for post-route optimizations. In a shape-based or gridlesssystem, the layout may be a gridless layout, which means there is nogrid which structures or polygon of the layout are associated with,other than a grid for the relevant manufacturing process, if any.

In an embodiment, the structure of database 301 facilitates shape-basedoperations. For example, a structure of this database may include anobstacle tree having nodes and leaves containing the obstacles of anintegrated circuit. This tree structure permits rapid determination ofwhere obstacles are when doing operations on the database, such asrouting nets.

In FIG. 3, the EDA system 300 includes one or more of the componentsdiscussed below, in any combination. One skilled in the art willrecognize that one or more of components shown in FIG. 3 may not berequired to practice specific aspects of present invention. For example,when DSM process engine 320 is omitted from system, the system couldstill perform automatic routing of interconnect, but without providingDRC checking capabilities.

A graphical user interface 302 provides users a graphical interface inwhich to perform operations on the integrated circuit design. Forexample, the user can view the integrated circuit using the graphicalinterface. The user may use the mouse and cursor to select a particularpolygon or feature, such as a net. The user may expand or zoom intoareas of the integrated circuit design.

A global router 304 is an automatic routing engine that coarsely routesinterconnects of the integrated circuit, thus enabling large designs tobe routed more rapidly and completely. The global router may alsoprovide visual and quantitative analysis of the congestion in the designby highlighting problem areas that can be fixed by incrementaladjustments to the floor plan. The global router is sometimes referredto as a coarse router because it provides generally the routes for theinterconnect, and may work in conjunction with a detail router 308(discussed below) to place the geometries of the interconnect.

A manual editor 306 is a shape-editing suite for creating or editingmetal, keep-outs, routing areas, and the ability to partition a designinto smaller areas. These areas can then be worked upon individually andcan be recombined at a later stage to complete the design. Full on-linedesign rule checking (DRC) ensures that manual operations are completederror-free first time. Powerful tools automatically push-aside existingwiring to make way for new wires and semiautomatic routing tools quicklyclose down troublesome nets by allowing the user to guide the routingengine around complex areas of the design.

The detail router 308 is an automatic router that completes the wiringin a design by determining the specific routes for each interconnect.The detail router may complete a portion of the wiring for design, suchas for sections or specified cells of the design, or may complete allthe wiring of the design. The detail router may route starting fromscratch or from partially completed routing. In an implementation, theglobal router determines the general route paths for the interconnect,and the detail router takes this routing information from the globalrouter and puts in the physical detailed geometries of the tracks andvias.

An engineering change order (ECO) engine 310 provides a capability tohandle late stage ECO changes. Every element of the design can bemodeled incrementally, thus eliminating the need to ever restart thephysical design, no matter what changes may need to be made fromupstream or downstream processes in the design. ECO engine capabilitiescan include the ability to shove or push cells aside to make space fornew or relocated instances, and the ability to drop groups of componentsand automatically find legal placement sites for them minimizing thedisruption to the design. When pushing or pulling cells, the wiresremain connected to the cells and the wires lengthen, shorten, and moveas needed, if possible, to keep the connections. The detail router canthen repair any violating interconnects and stitch-up any newlyintroduced interconnects, with minimum impact, ensuring circuitstability is never compromised.

A timing-driven routing engine 312 provides RC timing analysis ofinterconnects. Used in concert with the detail router, the timing enginecan determine the path of least delay for critical nets. Furthermore,the timing engine, in concert with an extraction engine, can activelyselect a longer path with a lower associated delay (e.g., due to lowercapacitance) in preference to a shorter but slower route.

An extraction engine 314 is provided. Utilizing a unified, high-speed RCextraction engine, the crosstalk functionality accurately calculates thecoupling between victim and aggressor signals. This same technology isthen used to identify potential problems, and automatically implements aDRC correct solution without changing the path of the signalunnecessarily. In addition, signal-to-signal (or within and betweenclasses of signals) spacing rules can be applied, and fully controllableautomatic shielding can be used to protect particularly sensitivesignals. The user is provided with unprecedented control over theresistance and capacitance in the signal path. Again, using the advancedbuilt-in RC extraction technology, the user can separately control pathresistance and capacitance, which is particularly useful for analog andmixed signal design.

In an implementation, the global router and detail router are linked tothe extraction engine. So, for example, when running, the global routeror detail router, or both, can call the extraction engine to obtain RCextraction information. The global router, detail router, or both, mayuse the RC extraction information when creating the interconnect routes.For example, the detail router may obtain RC extraction info from the RCengine in order determine whether an interconnect route meets currentdensity rules, and widen the interconnect width as needed. More detailsare discussed in U.S. patent application Ser. Nos. 10/709,843 and10/709,844, both filed Jun. 1, 2004 and incorporated by reference.

In a specific embodiment, an RC extraction driven constraints managerhas been enhanced to ensure matching on a per-layer basis as well as thewhole net or subnet. There is an increasing requirement in today'sdesigns to match length, time, resistance and capacitance across nets ona per-layer basis. This ensures total net constraints are met as beforebut also guarantees designated nets can match on a per-layer basis.

The tightly coupled, high-speed RC extraction engine is used both duringrouting (global router or detail router, or both) and for post-routingextraction to reach timing closure in record time. Integrated timinganalysis and curative features enable the management of delay within thedesign; the matching of delays within and between multiple nets; thesharing of delay between many nets in a signal path; and reducing thedelay in critical nets by minimizing resistance and capacitance.Intelligent lengthening increases the delay of the faster nets,preventing shoot-through.

The detail router can address current density issues in analog design,to help achieve an optimum routing result for the entire design, andsave valuable design time. The current information which is used todrive this current density functionality may come from, for example, afront-end schematic engine or simulation engine. The router canautomatically route a net at varying widths to guarantee sufficienttrack widths at every point in the topology of the net to carry allcurrent requirements. DRC and process checking tools locate anyinsufficient width areas that may exist in any routing, includingautomatically generated routing, manual routing, and importedprerouting.

A data export interface 316 is provided so data of the EDA system 300may be exported for other processes. For example, output from the EDAsystem may be passed through the export interface to other EDA systemsor software tools provided by other manufacturers. The export interfacewould provide output in a form, format, or structure, acceptable byprocess or software tool to which it is being exported.

A data import interface 318 provides the means to import data, such as acircuit layout, netlist, or design constraints. The data to be importmay be in various formats including data saved from other EDA systems orsoftware tools. In addition, the source of the data may be a database,floppy drive, tape, hard disk drive, CD-ROM, CD-R, CD-RW, DVD, or adevice over a communication network. Some examples of import formatsinclude text, ASCII, GDSII, Verilog, SIF, and LEF/DEF.

A DSM process engine 320 is provided. The DSM process engine does designrule checking (DRC). Design rule checking locates and highlights where adesign is breaking process design rules. For example, a design rule isthe minimum spacing between metal lines (i.e., geometries on a specificlayer). A design rule may be the minimum width of a metal line. A designrule may be a minimum polysilicon-to-diffusion spacing. There are manyother design rules for a typical process. Some design rules are forchecking geometries within a single layer, and some design rules are forchecking geometries of two or more layers.

A user may design an integrated circuit using a system such as shown inFIG. 3. A representative flow for designing an integrated circuit isoutlined in steps 1 to 8 below. Step 5 is further subdivided into threesubsteps.

Integrated Circuit Design Flow

1. Provide Circuit Specification

2. Create Circuit Design

3. Generate Netlist

4. Simulate Performance and Verify Functionality of Circuit Design

5. Generate Layout

5a. Layout Devices

5b. Connect Devices

5c. Connect Blocks of Circuitry

6. Physical Verification and Design Checking

7. Create Masks

8. Fabricate Integrated Circuit

Although the steps above are listed in a specific order, the steps maytake place in any order, as desired and depending on the specificapplication. These are general steps that may be applied to designing anintegrated circuit including custom, a gate array, standard cell, fieldprogrammable logic, microprocessor, digital signal processor,microcontroller, system-on-a-chip (SOC), memory, ASIC, mixed signal,analog, radio frequency (RF) or wireless, and others. There may beadditional or other steps, which may replace one or more above steps.Certain steps may be repeated. For example, after generating a layoutfor a circuit design, the step of simulating performance and verifyingfunctionality may be performed again. This time, the parasitics and RCconsiderations from the layout can be back-annotated into the netlist orcircuit design, and the design simulated again. The results of thissimulation will presumably be more accurate because more preciseinformation is provided.

Referring to FIG. 10, in step 1 (1005) of the flow, a circuitspecification is provided. This is a specification or description ofwhat the integrated circuit or circuit will do, and what the performancewill be. For example, the integrated circuit may be a memory integratedcircuit with particular address input pins and input-output (I/O) pins.Integrated circuit performance may be quantified terms in AC and DCperformance. For example, AC performance refers to propagation delays,maximum clock frequency, clock-to-output delay, hold time, and othersimilar parameters. DC performance refers to maximum supply current,maximum and minimum supply voltage, output current drive, and othersimilar parameters.

In step 2 (1008), an engineer creates a circuit design that presumablywill meet the circuit specification. This circuit design may includetransistors, resistors, capacitors, and other electronic components. Theengineer uses these electronic components as building blocks of thedesign, interconnecting them to achieve the desired functionality andperformance. The engineer may make a custom design using electroniccomponent building blocks or use a gate array, where the building blocksare sets of cells set by the gate array manufacturer. The design may beinput using a graphical design tool such as schematic capture program,and any other design tool may be used. The circuit may be describedusing a high-level design language (HDL). These design tools will createa netlist (step 3 (1012)) of the circuitry, which is a listing of thecomponents of the devices and their interconnections.

During the design phase, the engineer simulates the performance andverifies the functionality of the circuitry (step 4 (1014)). There aretransistor and process models to model the components. Some simulationtools include Spice, which performs circuit simulation, and Verilog,which performs functional and timing verification. This is where theelectrical information for current density routing is generated.

After deciding upon an initial circuit design, the engineer beginslayout (step 5 (1017)) of the circuitry. Layout refers to making thethree-dimensional dispositions of the element and interconnections tomake an integrated circuit. Making an integrated circuit is a layer bylayer process. Some layers of an integrated circuit are diffusion,polysilicon, metal-1, metal-2, contact, via, and others. There may bemultiple layers of the same material, but on different layers. Forexample, diffusion and polysilicon layers are used to make MOStransistors (step 5a). For example, metal-1 and metal-2 are twodifferent layers, where metal-1 is below the metal-2 layers. These metallayers may be connected together using a via. Metal is typically usedfor interconnections (step 5b) and supplying power and ground to thedevices.

Software tools may be used to help with the layout of the circuit, suchas the automatic routing of interconnect (steps 5b and 5c). Theinterconnect may be between devices. Devices and circuitry may begrouped into blocks or cells having inputs and outputs. The interconnectmay be between these blocks or cells (step 5b).

In step 6 (1021), after or while the layout is generated, the physicaldesign is verified and checked. For example, some of these operationsmay include layout-versus-schematic (LVS) checking, electrical rulechecking (ERC), design rule checking (DRC), layout simulation(especially for analog circuitry), power analysis, and timing analysis.Physical verification and design checking is often iterative. Based onthe design check, a design engineer or user may make changes to thedesign or layout, or both and the design may be rechecked in order tomake sure any areas of concern or design errors have been cleared.

The result of layout is data (e.g., provided in GDSII or other format)that is used to make the masks (step 7 (1023)). The masks are used tofabricate the integrated circuit (step 8 (1026)) using aphotolithography process. Typically, there are many “copies” of the sameintegrated circuited fabricated on the same wafer. Each integratedcircuit is a “die” on the wafer. Good dies are separated from the baddies. The good dies are sawed and packaged. Packaging generally includesencapsulating the die in plastic or other material, and connecting padsof the integrated circuit to pins of the package, where the integratedcircuit can be interfaced.

A basic flow of simultaneous place and route for analog designs is asfollows. A specific flow example is presented below, but it should beunderstood that the invention is not limited to the specific flows andsteps presented. A flow of the invention may have additional steps (notnecessarily described in this application), different steps whichreplace some of the steps presented, fewer steps or a subset of thesteps presented, or steps in a different order than presented, or anycombination of these. Further, the steps in other implementations of theinvention may not be exactly the same as the steps presented and may bemodified or altered as appropriate for a particular application or basedon the data.

1. Generate a random normalized polish expression.

2. Generate the associated placement and routing, along with its “cost.”That is, how good a potential placement/routing solution the polishexpression gives.

This step lists a place and route the design described by the polishexpression from the bottom up. That is, we write the normalized polishexpression as a skewed slicing tree and begin by placing and routingeach pair of leaves in the tree.

Placement will be as per the simulated annealing floor-planning methods,in that each cell may be placed in either of the rectilinear rotationsand the cells are placed either one above the other (when the polishexpression specifies a horizontal split) or side by side (when thepolish expression specifies a vertical split). This gives severaloptions, which must now be routed using a combination of traditionalrouting techniques and detection of specific patterns. At this stage wecan calculate an intermediate cost for the candidate solutions, andprune unpromising branches. The cost function will be based on the wirelength and whitespace. Note that there may be multiple equally goodroutings which we must retain at this stage.

We can now continue up the tree, combining child solutions in a similarmanner. This ultimately results in a fully placed and routed candidatesolution, with a corresponding cost.

3. Perform simulated annealing on the normalized polish expression withthe standard perturbations (as per the well-known simulated annealingapproach to floor planning). Each polish expression encountered duringthe process is placed and routed as in the previous step, which alsoprovides the cost function.

FIGS. 4A and 4B show an example of a simultaneous place and route. Anexample of a placed and routed layout for the normalized polishexpression 12H34HV56V7HV. The skewed slicing tree equivalent to thisexpression is shown, with the circled areas of the layout diagramcorresponding to the branches of the tree.

We place and route this example (as well as calculating its cost forsimulated annealing) beginning at the bottom of the tree. So, we startby placing and routing cells 1 and 2, cells 3 and 4, and cells 5 and 6.Cells 1 and 2 are split horizontally so they are placed one above theother, as are cells 3 and 4. Cells 5 and 6 are split vertically, so theyare placed side by side.

This process is likely to result in more than one possible layout ineach case.

We proceed up the tree, combining all combinations of the candidatesolutions we've obtained. That is, we combine all the possibilities forthe placement and routing of 1 and 2 with all those for 3 and 4, and wecombine all those for 5 and 6 with 7.

At each stage we calculate the intermediate cost (in terms of wirelength and whitespace) of each sub-layout, and we may prune anyunpromising candidates.

Finally we combine both sides of the tree to create a fully placed androuted solution of lowest cost.

FIGS. 5A-5B show an example of a simultaneous place and route. Anexample of a layout for the normalized polish expression 12H34H5HV.Again, the corresponding skewed slicing tree is shown along with theresulting layout diagram, where the branches of the tree are circled.

Here we begin by placing cells 1 and 2, and cells 3 and 4, both with ahorizontal split (i.e., one above the other). We then find the routingsof lowest possible cost. Next we place and route cell 5 with the resultsof combining 3 and 4. As in the previous example, this process will leadto multiple admissible solutions.

Finally we construct a fully placed and routed layout by combining thetwo halves of the tree that we have already calculated. At this point wetake the single lowest cost layout from all the possibilities.

FIGS. 6A-6B show an example of a simultaneous place and route. Here isan example of two possible placements/routings for two cells combinedwith a vertical split. In this case, the solution on the left (FIG. 6A)has the lowest cost.

FIGS. 7A-7C show an example of a simultaneous place and route. Here arethree possible placements/routings for two cells combined with ahorizontal split. The leftmost layout (FIG. 7A) has the lowest cost.

FIGS. 8A-8B show an example of a simultaneous place and route. Here wecombine two copies of the result of example in FIGS. 6A-6B, with eithera vertical or horizontal split.

FIGS. 9A-9D show an example of a simultaneous place and route. We willoften look for predetermined patterns that we can route in a manneroptimized for analog designs. These figures show an example of somepatterns.

This description of the invention has been presented for the purposes ofillustration and description. It is not intended to be exhaustive or tolimit the invention to the precise form described, and manymodifications and variations are possible in light of the teachingabove. The embodiments were chosen and described in order to bestexplain the principles of the invention and its practical applications.This description will enable others skilled in the art to best utilizeand practice the invention in various embodiments and with variousmodifications as are suited to a particular use. The scope of theinvention is defined by the following claims.

The invention claimed is:
 1. A method comprising: generating a firstexpression; using a computer processor, using the first expression,generating a first place-and-route solution for an integrated circuitdesign, wherein the integrated circuit design comprises a plurality ofcells, and the first place-and-route solution can comprise aninterconnect routing path formed on different interconnect layers;generating a second expression; using the second expression, generatinga second place-and-route solution for the integrated circuit design;generating a third expression; using the third expression, generating athird place-and-route solution for the integrated circuit design,wherein each of the first, second, and third place-and-route solutionsare different from each other; calculating a first cost function for thefirst place-and-route solution; calculating a second cost function forthe second place-and-route solution; calculating a third cost functionfor the third place-and-route solution; comparing the first, second, andthird cost functions based on at least one of wire length or whitespaceparameters; and based on the comparison of the first, second, and thirdcost functions, selecting one of the first, second, and thirdplace-and-route solutions to obtain a selected place-and-route solution,and discarding the place-and-route solutions not selected.
 2. The methodof claim 1 comprising: placing each cell of the selected place-and-routesolution adjacent to each other in a direction based on the expressionassociated with the selected place-and-route solution.
 3. The method ofclaim 1 wherein the first expression comprises a random normalizedpolish expression.
 4. The method of claim 1 wherein each of the first,second, and third expressions comprises a random normalized polishexpression.
 5. The method of claim 1 wherein for the firstplace-and-route solution for a horizontal split, a first cell has afirst edge and a second cell has a second edge, and a first interconnectextends directly from the first edge to the second edge without a90-degree turn, and the first edge is parallel to the second edge. 6.The method of claim 5 wherein for the second place-and-route solutionfor a horizontal split, a second interconnect extends from the firstedge to the second edge having at least one 90-degree turn, and thefirst edge is transverse to the second edge.
 7. The method of claim 6wherein for the third place-and-route solution for a horizontal split, athird interconnect extends from the first edge to the second edge havingat least two 90-degree turns, and the first and second edges aretransverse to the horizontal split.
 8. The method of claim 1 wherein forthe first place-and-route solution for a horizontal split, a first cellhas a first edge and a second cell has a second edge, the first andsecond edges are separated by a space and parallel to each other, and afirst interconnect extends between the first edge to the second edgewithout a 90-degree turn; for the second place-and-route solution for ahorizontal split, the first edge is oriented transverse to the secondedge, and a second interconnect extends from the first edge to thesecond edge having at least one 90-degree turn; and for the thirdplace-and-route solution for a horizontal split, the first edge isparallel to the second edge, and a third interconnect extends from thefirst edge to the second edge having at least two 90-degree turns. 9.The method of claim 1 wherein for the first place-and-route placement, avertical split comprises a first interconnect routing path comprising afirst cell and a second cell with a space between the cells, the firstcell comprises first, second, third and fourth edges, the first edge isopposite of the third edge, the second edge is opposite of the fourthedge, the second cell comprises fifth, sixth, seventh, and eighth edges,the fifth edge is opposite to the seventh edge, the sixth edge isopposite of the eighth edge, the space is between the second and eighthedges and bounded by a first line passing through the first and fifthedges, and a second line passing through third and seventh edges, and asecond interconnect is routed from the second edge to the eighth edge,at least a portion of the second interconnect is in the space andextends parallel to the second and eighth edges, and a portion of thesecond interconnect is in the space and extends transverse to the secondand eighth edges.
 10. The method of claim 9 wherein for the secondplace-and-route placement, a vertical split comprises a secondinterconnect routing path comprising a third cell and a fourth cell thatare placed adjacent to each other, the third cell comprises first,second, third and fourth edges, the first edge is opposite to the thirdedge, the second edge is opposite of the fourth edge, the fourth cellcomprises fifth, sixth, seventh, and eighth edges, the fifth edge isopposite to the seventh edge, the sixth edge is opposite of the eighthedge, the second edge touches the eighth edge, and a third interconnectis routed from the first edge to the fifth edge, wherein at least aportion of the third interconnect extends parallel to the first andfifth edges, and a portion of the third interconnect extends transverseto the first and fifth edges.
 11. A method of forming an integratedcircuit comprising the method of claim
 1. 12. A method of forming aphotolithography mask comprising the method of claim
 1. 13. A methodcomprising: generating a first expression; using a computer processor,using the first expression, generating a first place-and-route solutionfor an integrated circuit design, wherein the integrated circuit designcomprises a plurality of cells, and the first place-and-route solutioncan comprise an interconnect routing path formed on differentinterconnect layers; generating a second expression; using the secondexpression, generating a second place-and-route solution for theintegrated circuit design; generating a third expression; using thethird expression, generating a third place-and-route solution for theintegrated circuit design, wherein each of the first, second, and thirdexpressions comprises a random normalized polish expression, and each ofthe first, second and third place-and-route solutions are different fromeach other; calculating a first cost function for the firstplace-and-route solution; calculating a second cost function for thesecond place-and-route solution; calculating a third cost function forthe third place-and-route solution; comparing the first, second, andthird cost functions based on at least one of wire length or whitespaceparameters; and based on the comparison of the first, second, and thirdcost functions, selecting one of the first, second, and thirdplace-and-route solutions to obtain a selected place-and-route solution.14. The method of claim 13 comprising: placing each cell of the selectedplace-and-route solution adjacent to each other in a direction based onthe expression associated with the selected place-and-route solution.15. The method of claim 14 wherein for the first place-and-routesolution, a first cell has a first edge and the second cell has a secondedge, the first and second edges are parallel to each other and a firstinterconnect extends between the first edge to the second edge without a90-degree turn.
 16. The method of claim 15 wherein for the secondplace-and-route solution, the first edge is oriented transverse to thesecond edge, and a second interconnect extends from the first edge tothe second edge having at least one 90-degree turn.
 17. The method ofclaim 16 wherein for the third place-and-route solution, the first edgeis parallel to the second edge, and a third interconnect extends fromthe first edge to the second edge having at least two 90-degree turns.18. A method of forming an integrated circuit comprising the method ofclaim
 13. 19. A method of forming a photolithography mask comprising themethod of claim 13.